Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions?

Carmit Hazay; Rafael Pass; Muthuramakrishnan Venkitasubramaniam

doi:10.1007/978-3-030-45727-3_20

Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions?

Carmit Hazay, Rafael Pass, Muthuramakrishnan Venkitasubramaniam

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We prove that if a language L has a 4-round fully black-box zero-knowledge argument with negligible soundness based on one-way functions, then (Formula presented). Since (Formula presented) implies that the polynomial hierarchy collapses, our result implies that NP-complete languages are unlikely to have 4-round fully black-box zero-knowledge arguments based on one-way functions. In TCC 2018, Hazay and Venkitasubramaniam, and Khurana, Ostrovsky, and Srinivasan demonstrated 4-round fully black-box zero-knowledge arguments for all languages in NP based on injective one-way functions. Their results also imply a 5-round protocol based on one-way functions. In essence, our result resolves the round complexity of fully black-box zero-knowledge arguments based on one-way functions.

Original language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Editors	Anne Canteaut, Yuval Ishai
Publisher	Springer
Pages	599-619
Number of pages	21
ISBN (Print)	9783030457266
DOIs	https://doi.org/10.1007/978-3-030-45727-3_20
State	Published - 2020
Event	39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia Duration: 10 May 2020 → 14 May 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12107 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020
Country/Territory	Croatia
City	Zagreb
Period	10/05/20 → 14/05/20

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2020.

Funding

The first author is supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant 1316/18. The second author is supported in part by NSF Award SATC-1704788, NSF Award RI1703846, and AFOSR Award FA9550-18-1-0267, and in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2019-19-020700006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. The third author is supported by Google Faculty Research Grant and NSF Award CNS-1618884. The views expressed are those of the authors and do not reflect the official policy or position of Google, the Department of Defense, the National Science Foundation, or the U.S. Government.

Funders	Funder number
National Science Foundation	RI1703846, SATC-1704788, 1704788
U.S. Department of Defense
Air Force Office of Scientific Research	FA9550-18-1-0267
Google	CNS-1618884
Office of the Director of National Intelligence
Intelligence Advanced Research Projects Activity	2019-19-020700006
Israel Science Foundation	1316/18

Keywords

Black-box constructions
One-way functions
Zero-knowledge arguments

Access to Document

10.1007/978-3-030-45727-3_20

Cite this

Hazay, C., Pass, R., & Venkitasubramaniam, M. (2020). Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions? In A. Canteaut, & Y. Ishai (Eds.), Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (pp. 599-619). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12107 LNCS). Springer. https://doi.org/10.1007/978-3-030-45727-3_20

Hazay, Carmit ; Pass, Rafael ; Venkitasubramaniam, Muthuramakrishnan. / Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions?. Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. editor / Anne Canteaut ; Yuval Ishai. Springer, 2020. pp. 599-619 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We prove that if a language L has a 4-round fully black-box zero-knowledge argument with negligible soundness based on one-way functions, then (Formula presented). Since (Formula presented) implies that the polynomial hierarchy collapses, our result implies that NP-complete languages are unlikely to have 4-round fully black-box zero-knowledge arguments based on one-way functions. In TCC 2018, Hazay and Venkitasubramaniam, and Khurana, Ostrovsky, and Srinivasan demonstrated 4-round fully black-box zero-knowledge arguments for all languages in NP based on injective one-way functions. Their results also imply a 5-round protocol based on one-way functions. In essence, our result resolves the round complexity of fully black-box zero-knowledge arguments based on one-way functions.",

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Hazay, C, Pass, R & Venkitasubramaniam, M 2020, Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions? in A Canteaut & Y Ishai (eds), Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12107 LNCS, Springer, pp. 599-619, 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020, Zagreb, Croatia, 10/05/20. https://doi.org/10.1007/978-3-030-45727-3_20

Which languages have 4-round fully black-box zero-knowledge arguments from one-way functions? / Hazay, Carmit; Pass, Rafael; Venkitasubramaniam, Muthuramakrishnan.
Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. ed. / Anne Canteaut; Yuval Ishai. Springer, 2020. p. 599-619 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12107 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review